Whichのほうが自然ですね。なぜ？と聞かれると、難しいですが。。
恐らく：
This is a game.
I am quite ignorant of its rules.
This is a game whose rules I am quite ignorant of.
whose→whichになります。
別の例を挙げると：
the house whose roof is painted red => the house, of which the roof is painted red
